The equation is: $$\sin^2(x)-(3/4)$$
How do you get this equation in an alternate form, so that there is only division or multiplication present between trigonometric functions.
The solution is: $$\sin(x+π/3)\sin(x-π/3)$$
My try: $$\sin^2(x)-(1/2)-(1/2)*(1/2) = \sin^2(x)-\sin(π/6)-\sin(π/6)*\sin(π/6)$$
Beyond this point I don't know what to do, to get the correct answer
Thank you very much for help
HINT
$$\sin^2 x-\frac34 = \left( \sin x+\frac{\sqrt 3}{2} \right) \left(\sin x-\frac{\sqrt 3}{2} \right)$$
and
$$\sin \frac{\pi}{3}=\frac{\sqrt 3}{2}$$